Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2026

A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes

Résumé

In this article, we extend the Boltzmann framework for polyatomic gases by introducing quasi-resonant kernels, which relax resonant interactions, for which kinetic and internal energies are separately conserved and lead to equilibrium states with two temperatures. We establish an H-theorem and analyze the quasi-resonant model's asymptotic behaviour, demonstrating a two-phase relaxation process: an initial convergence towards a two-temperature Maxwellian state followed by gradual relaxation of the two temperatures towards each other. Numerical simulations validate our theoretical predictions. The notion of quasi-resonance provides the first rigorous framework of a Boltzmann dynamics for which the distribution is at all times close to a multi-temperature Maxwellian, relaxing towards a one-temperature Maxwellian.

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hal-05095531 , version 1 (03-06-2025)

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Thomas Borsoni, Laurent Boudin, Julien Mathiaud, Francesco Salvarani. A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes. ESAIM: Mathematical Modelling and Numerical Analysis, 2026, 60 (2), pp.473-494. ⟨10.1051/m2an/2026008⟩. ⟨hal-05095531⟩
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